Finite Group Databasebeta

← #14285408

Subgroups — #14285408

Order 1920.

404 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754174C211yesmaximal, characteristic
2#11752416C211yesmaximal, characteristic
3C3×#65758C211yesmaximal, characteristic
4#11746511C212yesmaximal, complemented
5#11746509C212yesmaximal, complemented
6#10604520—31nomaximal, Hall
7C2×C3×#704—21no—
8#91813C411yescharacteristic
9C5×#924C411yescharacteristic
10C2×C3×C4×Dic5C2211yescharacteristic
11#91574—21no—
12#91528—21no—
13#91468C2211yescharacteristic
14#91378—21no—
15#91376C2211yescharacteristic
16#91333C411yescharacteristic
17Dic5×Dic6C411yescharacteristic
18#91323—21no—
19#91241—21no—
20#91233C2212yes—
21#91231—21no—
22C3×#4004C2212yes—
23C3×C4⋊#170—21no—
24#70510—51nomaximal, Hall
25#65956—31no—
26#65758D311yescharacteristic
27#65757—31no—
28#64931—32no—
29#64873—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×Dic30C2×C411yescharacteristic
32C2×C5×Dic6C2×C411yescharacteristic
33C22×C3×Dic5D411yescharacteristic
34C22×C3×Dic5D411yescharacteristic
35C2×#1204—21no—
36C2×C3⋊#170—22no—
37C3×#704—42no—
38C2×C3×#170—22no—
39#6719—21no—
40C4⋊Dic15C2×C411yescharacteristic
41#6712—21no—
42C5×#217—21no—
43C5×C4⋊Dic3C2×C411yescharacteristic
44C5×Dic3⋊C4—21no—
45C3×C4×Dic5C2×C411yescharacteristic
46C3×C4×Dic5D411yescharacteristic
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5C2311yescharacteristic
49Dic3⋊Dic5—21no—
50#6669—21no—
51#6668—21no—
52#6668—21no—
53#6668—21no—
54Dic3×Dic5—21no—
55Dic3×Dic5—21no—
56#5470—51no—
57C3×#423—51no—
58#4926—51no—
59#4482—52no—
60#4481—52no—
61C2×#704—21no—
62C5×C22⋊Q8—31no—
63Q8×Dic5—31no—
64#4090—31no—
65#4070—31no—
66C2×C4×Dic5C2×D311yescharacteristic
67#4035—61no—
68#4034—31no—
69#4033—31no—
70#4033—61no—
71#4024—61no—
72#4023—61no—
73C22⋊#170—61no—
74#4004—32no—
75#4004C2×D312yes—
76#4002—61no—
77C4⋊#170—21no—
78#1559—151noSylow
79C23×C3×C5C22⋊C411yescharacteristic
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×Dic15—21no—
84C2×Dic15—21no—
85Dic30—41no—
86C2×C5×Dic3—21no—
87C2×C5×Dic3—21no—
88C5×Dic6—41no—
89C2×C3×Dic5—21no—
90C2×C3×Dic5—21no—
91C2×C3×Dic5—22no—
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C22⋊C411yescharacteristic
94C2×C3×Dic5C2×D411yescharacteristic
95C2×C3×Dic5C2×D411yescharacteristic
96#1204—41no—
97#1204—41no—
98C3⋊#170—42no—
99C3×#170—42no—
100C2×C3×M16—101no—
101C2×C3×C42—51no—
102#926—101no—
103#924—51no—
104#924—101no—
105#924AGL(1,𝔽5)11yescharacteristic
106#870—101no—
107#869—51no—
108#869—51no—
109C4×Dic6—51no—
110C4×Dic6—51no—
111C4×Dic6—101no—
112C3×C4⋊C8—52no—
113C3×C4⋊C8—101no—
114#830—101no—
115C4⋊(C3⋊C8)—52no—
116#803—101no—
117C2×C5×Q8—31no—
118C22×C4×C5C4×D311yescharacteristic
119C22×Dic5D1211yescharacteristic
120C22×Dic5#6711yescharacteristic
121C2×Dic10—31no—
122C2×Dic10—61no—
123#704—42no—
124C2×#170—22no—
125C2×#170—62no—
126C5×C4⋊C4—31no—
127C5×C4⋊C4—61no—
128C5×C22⋊C4—61no—
129C22⋊Dic5—61no—
130C4⋊Dic5—31no—
131C4⋊Dic5—61no—
132#683—61no—
133#683—61no—
134#683—61no—
135#683—61no—
136#683—61no—
137C4×Dic5—61no—
138C4×Dic5—61no—
139C4×Dic5C4×D311yescharacteristic
140C4×Dic5D1211yescharacteristic
141C4×Dic5#6711yescharacteristic
142C4×Dic5C22×D311yescharacteristic
143#533—151no—
144#432—151no—
145#423—51no—
146#333—152no—
147#332—152no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5C2×C22⋊C411yescharacteristic
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154Dic15—41no—
155Dic15—41no—
156C3×Dic5—21no—
157C3×Dic5—21no—
158C3×Dic5AGL(1,ℤ/8)11yescharacteristic
159C3×Dic5#13712yes—
160C3×Dic5#13711yescharacteristic
161C5×Dic3—41no—
162C5×Dic3—41no—
163C22×C3×C4—51no—
164C22×C3×C4—51no—
165C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
166C2×Dic6—51no—
167C2×Dic6—101no—
168C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
169C3×M16—202no—
170C2×C3×C8—102no—
171C3×C42—51no—
172C3×C42—51no—
173C3×C42—51no—
174C3×C42—51no—
175#217—21no—
176#217—101no—
177C4⋊Dic3—51no—
178C4⋊Dic3—101no—
179C4⋊Dic3—101no—
180C4⋊Dic3—101no—
181C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
182Dic3⋊C4—21no—
183Dic3⋊C4—101no—
184Dic3⋊C4—101no—
185Dic3⋊C4—101no—
186C4×Dic3—101no—
187C4×Dic3—101no—
188C2×C3⋊C8—102no—
189C23×C5(C2×D3)⋊C411yescharacteristic
190C5×Q8—121no—
191C2×C4×C5—41no—
192C2×C4×C5—61no—
193C2×C4×C5—61no—
194C2×C4×C5(C2×D3)⋊C411yescharacteristic
195C2×C4×C5C2×C4×D311yescharacteristic
196C2×Dic5—22no—
197C2×Dic5—21no—
198C2×Dic5—21no—
199C2×Dic5—61no—
200C2×Dic5—61no—
201C2×Dic5(C2×D3)⋊C411yescharacteristic
202C2×Dic5(C2×D3)⋊C411yescharacteristic
203C2×Dic5C2×D1211yescharacteristic
204C2×Dic5C2×#6711yescharacteristic
205Dic10—121no—
206Dic10—121no—
207Dic10—121no—
208#170—42no—
209#170—122no—
210C2×M16—101no—
211C4⋊Q8—151no—
212C4⋊Q8—151no—
213#125—301no—
214C22⋊Q8—31no—
215C22⋊Q8—151no—
216C22⋊Q8—301no—
217C4×Q8—151no—
218C4×Q8—151no—
219C4×Q8—301no—
220#117—301no—
221C2×C42—51no—
222C4⋊C8—52no—
223C4⋊C8—101no—
224C4⋊C8—152no—
225C22⋊C8—301no—
226#97—301no—
227C2×C3×C5—41no—
228C2×C3×C5#41311yescharacteristic
229C2×C3×C5#41711yescharacteristic
230C2×C3×C5#41911yescharacteristic
231C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
232C2×C3×C4—41no—
233C2×C3×C4—51no—
234C2×C3×C4—51no—
235C2×C3×C4—51no—
236C2×C3×C4—51no—
237C2×C3×C4—101no—
238C2×C3×C4—101no—
239C2×C3×C4—102no—
240C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
241C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
242C2×Dic3—21no—
243C2×Dic3—21no—
244C2×Dic3—101no—
245C2×Dic3—101no—
246Dic6—41no—
247Dic6—201no—
248Dic6—201no—
249Dic6—201no—
250C3×C8—202no—
251C3⋊C8—202no—
252C22×C5—21no—
253C22×C5—21no—
254C22×C5—21no—
255C22×C5C2×(C2×D3)⋊C411yescharacteristic
256C4×C5—21no—
257C4×C5—21no—
258C4×C5—121no—
259C4×C5—121no—
260Dic5—21no—
261Dic5—21no—
262Dic5—121no—
263Dic5—121no—
264Dic5#90912yes—
265Dic5#93211yescharacteristic
266Dic5#94211yescharacteristic
267C2×Q8—31no—
268C2×Q8—151no—
269C2×Q8—301no—
270C22×C4—51no—
271C22×C4—51no—
272C22×C4D3×AGL(1,𝔽5)11yescharacteristic
273M16—202no—
274C2×C8—102no—
275C2×C8—302no—
276C4⋊C4—31no—
277C4⋊C4—61no—
278C4⋊C4—151no—
279C4⋊C4—301no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C4⋊C4—301no—
283C4⋊C4—301no—
284C4⋊C4—301no—
285C22⋊C4—61no—
286C22⋊C4—301no—
287C42—51no—
288C42—51no—
289C42—51no—
290C42—51no—
291C42—301no—
292C42—301no—
293C3×C5#155911yescharacteristic, complemented, Hall
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—51no—
301C3×C4—51no—
302C3×C4—52no—
303C3×C4—101no—
304C3×C4—101no—
305Dic3—41no—
306Dic3—41no—
307Dic3—201no—
308Dic3—201no—
309C2×C5—41no—
310C2×C5#496611yescharacteristic
311C2×C5#512011yescharacteristic
312C2×C5#513211yescharacteristic
313C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
314Q8—121no—
315Q8—601no—
316Q8—601no—
317Q8—601no—
318C2×C4—41no—
319C2×C4—51no—
320C2×C4—51no—
321C2×C4—51no—
322C2×C4—51no—
323C2×C4—61no—
324C2×C4—61no—
325C2×C4—101no—
326C2×C4—101no—
327C2×C4—102no—
328C2×C4—301no—
329C2×C4—301no—
330C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
331C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
332C8—202no—
333C8—602no—
334C2×C3—41no—
335C2×C3#6577711yescharacteristic
336C2×C3#6578211yescharacteristic
337C2×C3#6579311yescharacteristic
338C5#7051011yescharacteristic, complemented, Sylow
339C22—21no—
340C22—21no—
341C22—21no—
342C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
343C4—21no—
344C4—21no—
345C4—51no—
346C4—51no—
347C4—52no—
348C4—101no—
349C4—101no—
350C4—121no—
351C4—121no—
352C4—601no—
353C4—601no—
354C3#1060452011yescharacteristic, complemented, Sylow
355C2—41no—
356C2#1175170511yescharacteristic
357C2#1175171211yescharacteristic
358C2#1175200811yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1559
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #11746511C2semidirect
5. #11746509C2semidirect
293. C3×C5#1559semidirect
338. C5#70510semidirect
354. C3#10604520semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117541742
#117524162
C3×#657582
#117465112
#117465092
#106045203
#705105